Intuitive everyday logic does work a bit different This is true. Intuitive everyday logic does work a bit different in most people from propositional and

Intuitive everyday logic does work a bit different This is true. Intuitive everyday logic does work a bit different in most people from propositional and first-order logic, in particular with regards to or and implies. For example, most people's or is the exclusive or you mention. But both logics can explain each other. For example, not, and as well as for all is pretty similar in formal and informal logic, and, as you know, those three are a basis for all of (first order) logic.